Global well - posedness and scattering for the focusing, energy - critical nonlinear Schrödinger problem in dimension $d=4$ for initial data below a ground state threshold

Abstract

In this paper we prove global well - posedness and scattering for the focusing, energy - critical nonlinear Schrödinger initial value problem in four dimensions. Previous work proved this in five dimensions and higher using the double Duhamel trick. In this paper, using long time Strichartz estimates we are able to overcome the logarithmic blowup in four dimensions.

39 pages

References in corpus (1)

• The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher

Cited by in corpus (4)

• The radial defocusing energy-supercritical NLS in dimension four
• Computing solutions of Schrödinger equations on unbounded domains- On the brink of numerical algorithms
• Global Dynamics of solutions with group invariance for the nonlinear Schrödinger equation
• Scattering for the mass super-critical perturbations of the mass critical nonlinear Schrödinger equations